Soft Cells and the Geometry of Seashells

The article discusses a new class of geometric shapes called "soft cells," which are designed to minimize sharp corners and better represent the complex tiling patterns found in nature, particularly in biological structures like seashells. Traditional geometric tilings, which include shapes with flat faces and sharp corners, are insufficient for modeling the highly curved forms observed in natural phenomena. The authors introduce "soft tilings," which consist of cells with curved faces that fill space while reducing the number of sharp corners. They demonstrate that these soft tilings can be derived from traditional polyhedral tilings through smooth deformations. The research highlights the abundance of these soft shapes in nature, linking them to various biological structures, including the chambers of the Nautilus shell. The study emphasizes the importance of understanding these geometric forms to better comprehend biological growth and structure.

- Soft cells represent a new class of geometric shapes minimizing sharp corners.

- Traditional tilings with flat faces are inadequate for modeling natural forms.

- Soft tilings can be derived from polyhedral tilings through smooth deformations.

- The research connects soft tilings to biological structures, such as seashells.

- Understanding soft tilings enhances insights into biological growth and geometry.